the grout diffusion radius (grouting hole spacing) and the
effect of the grouting. The analysis results were still far away
from the engineering requirements.
In this paper, a fracture network of rock mass was estab-
lished for dual medium grouting by Monte Carlo random
method. The finite element analysis was conducted for the
diffusion process in the fissure and the permeability of
rock mass after grouting. The grouting hole was accordingly
optimized and evaluated on the basis of analysis results.
The analysis was performed based on the diffusion motion
equation of cement grout in a single fracture, with full
consideration of various factors such as the time variability of
rheological parameters of cement grout, the opening change
and the fissure cracking in the grouting process, and the
precipitation of cement particles.
2. Diffusion Equations of Cement
Grout in the Single Fracture
2.1. Diffusion Equation.Cement grout in rock mass is essen-
tiallyatwo-phaseflowprocessofthegranularliquidinthe
fissures. According to the flow conservation and balance
equation, the diffusion motion equation of grout in the single
fissure can be deduced as follows [ 12 – 14 ]:
푢=−
퐽푏^2
2휂
[1−(
푧
푏
)
2
−2푧푏
푏
(1−
푧
푏
)], (1)
where푢is the velocity of the grout movement at a certain
cross-section point;푧is the distance of a certain point from
the center on the cross-section;푧푏is a half of the height of the
plug flow;푏isahalfofthefractureopeningonacross-section;
휂is the viscosity coefficient of the grout;퐽is the pressure
gradient.
To integrate the above equation along the fractured cross-
section, the grout flow in a single fracture at a certain moment
canbeobtainedasfollows:
푞푖=
2퐽푏^3
3휂
[1 −
3푧푏
2푏
+
1
2
(
푧푏
푏
)
3
]. (2)Obviously, by adding up all the fracture flow푞푖,the
injection rate of grouting at a certain moment,푈,isobtained,
namely,
푈=
푡
∑
푖푞푖. (3)
To make a time integration of the injection rate, grout
quantity,푄, can be obtained, namely,
푄=∫
푡0푡
∑
푖푞푖푑푡. (4)
When푡is the end time of grouting,푄is the total injection
amount of grout.
2.2. Evolution Rules of the Grouting Parameter.From the
diffusion equation of a single fissure, it can be seen that
the flow푞is dependent on the fracture opening, the pressure
gradient, and the rheological parameters of grout. All these
factors are always changing throughout the grouting process.2.2.1. Time Variation of the Rheological Parameters of Grout.
The rheological parameters of cement grout are time vary-
ing and depend significantly on the grouting time, the
water-cement ratio, and the water temperature. The pure
cement grout within the range of the commonly used water-
cement ratio is a typical Bingham rheological material, whose
essential features are having structural strength and time-
dependent performance [ 15 – 18 ]. To describe the grout rhe-
ological model approximately, the following linear equation
can be used:휏=휏 0 (푡)+휂(푡)
⋅
훾, (5)where휏and⋅
훾aretheshearstressandthestrainrateofgrout,
respectively;휏 0 (푡)and휂(푡)are the time-dependent yielding
strength (dynamic shear force) and the plastic viscosity of
grout, respectively.
Different water-cement ratios were used in the grouting
tests of Dagang Mountain Hydropower Station. The rheolog-
ical parameters and time curve were measured by the long
homemade capillary rheological parameter meter (Figure 1).2.2.2. Variation of Pressure Gradient.The rock fracture for
grouting is usually filled with groundwater. It was assumed
that there was not exchange between the grouting front
and the groundwater, and thus there was only hydrostatic
pressure. The grouting pressure, in addition to be affected by
the local head loss and frictional head loss, will push grout
flow in the fracture. Its gradient in the fracture is directly
dependent on the attenuation of grouting pressure and the
diffusion radius. The variation of pressure gradient could be
investigated in the numerical simulation of grout diffusion in
the fracture.2.2.3. Evolution law of the Fracture Opening.The fracture
opening is the principal variation in the diffusion equation,
which plays a leading role in the diffusion distance [ 19 ]. The
evolution law of the following five factors in the grouting pro-
cess directly affects the accuracy of the numerical simulation
for the diffusion distance.(1)Effect of the Fracture Roughness.Seepage channels of the
grout are mainly the fracture surfaces that are rough and
often contain parts of the cementation or filling. This leads
to complicated fracture opening with a large influence on
thefluidmotion.Inthefracturehydraulics,themechanical
opening of the fracture,2푏푚,isreplacedbytheequivalent
hydraulic opening,2푏ℎ, which is defined as follows: under
thesamepressuregradientandflowpattern,thevolumeflow
within the rough fracture is equal to that within the flat and
smooth fracture whose opening is2푏ℎ.2푏ℎcan be determined
comprehensively by the drilling hydraulic document and
water pressure test. As a virtual opening, the equivalent
hydraulic opening reflects the hydraulic characteristics of